Abstract:

A structure with trivial group of automorphisms is called rigid. The closeness of a structure to rigid one is described using the concept of semantic rigidity. The similar concept of syntactic rigidity of a structure measures the closeness of a given structure to a structure that is the definable closure of an empty set.

In this paper we study all possible values of quadruples of unar rigidity. This paper is a continuation of the paper, which described all possible pairs of $\exists$-syntactic and $\exists$-semantic rigidity of unars, as well as $\forall$-syntactic and $\forall$-semantic rigidity of unars.